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arXiv · 2007.09145

A de Branges-Beurling theorem for the full Fock space

Robert T. W. Martin·Eli Shamovich
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Abstract

We extend the de Branges-Beurling theorem characterizing the shift-invariant spaces boundedly contained in the Hardy space of square-summable power series to the full Fock space over $\mathbb{C} ^d$. Here, the full Fock space is identified as the \emph{Non-commutative (NC) Hardy Space} of square-summable Taylor series in several non-commuting variables. We then proceed to study lattice operations on NC kernels and operator-valued multipliers between vector-valued Fock spaces. In particular, we demonstrate that the operator-valued Fock space multipliers with common coefficient range space form a bounded general lattice modulo a natural equivalence relation.

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Robert T. W. Martin, Eli Shamovich. 2020-07-17. A de Branges-Beurling theorem for the full Fock space. https://arxiv.org/abs/2007.09145

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